ANOVA, Factorial ANOVA, and Multivariate Analysis Vocabulary

Vocabulary flashcards on ANOVA, Factorial ANOVA, and Multivariate Analysis based on the provided slide deck notes.

Multivariate Analysis

Statistical techniques used to study more complex sets of data than what univariate analysis methods can handle.

Software for Multivariate Analysis

Programs such as SPSS or SAS almost always required for multivariate analysis because working with data sets by hand can be overwhelming.

Type I Error Reduction

A benefit of multivariate analysis wherein performing multi-variable testing reduces the likelihood of falsely rejecting a true null hypothesis.

Principal Component Analysis (PCA)

A multivariate technique that decomposes a data table with correlated measures into a new set of uncorrelated measures.

Correspondence Analysis

A technique similar to Principal Component Analysis (PCA) that specifically applies to contingency tables.

Additive Trees, Multidimensional Scaling, and Cluster Analysis

Multivariate methods appropriate when the rows and columns in a data table represent the same units and the measure is either a similarity or a distance.

ANOVA Test

Analysis of Variance test; a way to find out if survey or experiment results are significant, determining whether to reject the null hypothesis or accept the alternate hypothesis.

One-Way ANOVA

An Analysis of Variance test that has one independent variable (with 2 levels) affecting a dependent variable.

Two-Way ANOVA

An extension of the One-Way ANOVA used when there are two independent categorical variables (factors) and one measurement quantitative outcome variable.

Groups or Levels

Different sub-categories or divisions within the same independent variable.

Nested ANOVA

An Analysis of Variance method used when the groups or levels have a hierarchical structure where each level has unique subgroups.

Replication in Two-Way ANOVA

Duplicating tests with multiple groups where individuals within a group undergo multiple conditions/tests, as opposed to testing without replication.

Factors

The independent categorical explanatory variables in a Two-Way ANOVA.

Treatment Groups

All possible combinations of factor levels in a factorial design (for example, 3 levels of income $\times$ 3 levels of gender = 9 treatment groups).

Main Effect

The calculated effect of a single factor in a Two-Way ANOVA considered separately, similar to a One-Way ANOVA.

Interaction Effect

The effect calculated in a Two-Way ANOVA where all factors are considered simultaneously.

Cell Observation Requirement for Two-Way ANOVA

If multiple observations are entered into cells to test interaction effects, the number of observations in each cell must be equal.

Third Null Hypothesis ($H_{03}$)

The additional hypothesis tested in Two-Way ANOVA with multiple observations per cell, stating that factors are independent or that no interaction effect exists.

Homoscedasticity

The assumption for Two-Way ANOVA that population variances across groups must be equal.

Cluster Analysis Visual Representation

A scatter plot illustrating data points categorized into distinct groupings or clusters (e.g., showing three groups).